Covering a Compact Set in a Banach Space by an Operator Range of a Banach Space with Basis
نویسندگان
چکیده
A Banach space X has the approximation property if and only if every compact set in X is in the range of a one-to-one bounded linear operator from a space that has a Schauder basis. Characterizations are given for Lp spaces and quotients of Lp spaces in terms of covering compact sets in X by operator ranges from Lp spaces. A Banach space X is a L1 space if and only if every compact set in X is contained in the closed convex symmetric hull of a basic sequence which converges to zero.
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